1. In the region $D$ shown below, the lower and upper boundaries are parametrized by $C^1$-functions:
$y = \phi_j(x)$ for $j = 1, 2$ and $a \le x \le b$. Let $P(x, y)$ be a $C^1$-function on a neighborhood of $D$.
$y = \phi_2(x)$
$D$
$y = \phi_1(x)$
Sketch a proof of the part of Green's theorem stating that $\iint_D \frac{\partial P}{\partial y}(x, y) dy dx = -\int_{\partial D^+} P(x, y) dx$.
